As part of its anti-immigrant drive, the Trump administration has deported thousands of Cubans, sending some to Mexico and even African countries, and others back to Cuba.

Now, U.S. officials are close to securing a new destination: Uruguay, the second-smallest country in South America, which already has a relatively large population of residents who migrated from Cuba.

The State Department under Secretary of State Marco Rubio, the son of Cuban immigrants, has been discussing the proposal with Uruguay’s foreign ministry for months, according to officials from both countries.

Uruguay entered the negotiations partly because it needs immigrant workers, and partly to win favor with the Trump administration, a senior Uruguayan official said.

But as the United States searches for countries willing to take in Cubans, it is also worsening the circumstances that have forced many Cubans to flee their country in the first place.

In recent months, the Trump administration’s economic pressure campaign has blocked oil shipments to the Caribbean island, which was already devastated by years of U.S. sanctions and misrule by its authoritarian leaders.

Mr. Rubio said the United States had many concerns about Cuba, which is 90 miles from Florida, including “the threat of mass migration.”

That is “always a risk that you run when countries are as deeply destabilized as Cuba,” he told reporters traveling with him in Manila last week.

In Uruguay, the government seeks to regularize Cuban migrants so they can find work opportunities and get social services. Many initially apply for asylum.

Some American officials think that could help ensure deportees do not try to return to the United States, while also allowing them to live outside Cuba, officials said.

A written agreement with Uruguay might not specify Cubans in the text, an official said, though in practice they would be the focus of deportations to that country.

Some of the Cubans in the United States might have relatives in Uruguay, and the governments are discussing the possibility of reuniting families, a foreign ministry official in Uruguay said. Like other officials interviewed for this article, he spoke on the condition of anonymity to discuss sensitive negotiations.

The Cuban government often has refused to take back citizens who have been deported from the United States, but it agreed to receive several flights this year.

The Trump administration told a federal court in March that it had sent 6,000 Cubans to Mexico, where many are struggling to find work. It has also sent Cuban migrants to Africa, including to Eswatini, formerly known as Swaziland, and war-ravaged South Sudan, where the migrants have been kept in detention centers.

The policy is part of a broad push by the Trump administration to find nations willing to take migrants and immigrants deported from the United States.

The State Department has been criticized for sending some deportees to distant countries where they have no connections, or where governments have records of human rights abuses.

Governments in South America have been reluctant to accept deportees. But Paraguay signed an agreement with the State Department last year and has accepted flights of deportees of various nationalities. Ecuador also signed an agreement last year, and the deportees sent there include Cubans.

Uruguay, a nation of 3.4 million, has long had a relatively open immigration policy.

“We have a tradition of welcoming people who come from other countries,” said Carlos Negro, the country’s interior minister. Uruguay, he added, “was born as an immigrant country.” Most Uruguayans are descended from colonial settlers and immigrants from Spain and Italy.

While migrants-rights groups have criticized Mr. Trump’s deportation policy, some have said that for Cuban deportees, ending up in Uruguay would be better than being sent to many other countries.

In March, Leydis Aguilera, who immigrated to Uruguay from Cuba 16 years ago, became a member of the national parliament. She has described the warm welcome she received in Uruguay and how she eventually found education and job opportunities there.

Uruguay needs to expand its work force to compensate for its small and aging population. Public opinion remains largely in favor of immigration, and deportations are rare. Even those who enter without a visa are often allowed to stay legally.

Last year, Uruguay had nearly 24,000 asylum seekers from Cuba, according to United Nations statistics.

The State Department declined to comment on the talks with Uruguay. “Implementing the Trump administration’s immigration policies is a top priority for the Department of State,” it said in a statement. “As Secretary Rubio has said, we remain unwavering in our commitment to end illegal and mass immigration and bolster America’s border security.”

The Uruguayan foreign ministry declined to comment.

During much of the Cold War, the U.S. government welcomed people from Communist-ruled Cuba and offered them a rapid pathway toward permanent residency and citizenship. The Cuban Adjustment Act of 1966 has compelled this of Democratic and Republican administrations.

But starting in the Clinton administration, American officials have found ways to work around or weaken the requirements of the law to try to avoid taking in an influx of migrants.

President Trump has accelerated that. His administration has blocked several routes to permanent residency status and citizenship for Cubans.

That puts 600,000 Cubans at risk of deportation, according to María José Espinosa, the executive director of the Center for Engagement and Advocacy in the Americas, which analyzes deportation data.

Ada Ferrer, a history professor at Princeton and author of a book on the history of Cuba, said “there was a time when they wouldn’t go after Cubans because of the Cuban Adjustment Act, but no one is abiding by that anymore.”

“If you ran on mass deportations, you’re going to try to do mass deportations,” she added. “But Cuban Americans thought they would be protected.”

A Cuban grandfather of Mr. Rubio who flew to the United States in 1962 without a visa got a deportation order, but was allowed to remain in the country after being granted refugee status, according to a biography of Marco Rubio by Manuel Roig-Franzia.

Yael Schacher, the director for the Americas and Europe at Refugees International, said that all deportation plans were “bad options,” especially those targeting people who have lived in the United States for a long time.

Still, she said, a Latin American country “with a well-functioning asylum system that is safe is like the least bad option.”

Despite Uruguay’s relative tolerance, migrants often struggle. Uruguay is expensive compared to other South American nations. Many Cubans initially live in boardinghouses while working as delivery or Uber drivers, caregivers and security guards.

Hamed Aleaziz and Eileen Sullivan contributed reporting from Washington.